Libby was explaining the consequences of his light-pressure drive to his new commanding officer. “The loci of our attainable destinations is contained in a sheaf of paraboloids having their apices tangent to our present course. This assumes that acceleration by means of the ship’s normal drive will always be applied so that the magnitude our present vector, just under the speed of light, will be held constant. This will require that the ship be slowly precessed during the entire maneuvering acceleration. But it will not be too fussy because of the enormous difference in magnitude between our present vector and the maneuvering vectors being impressed on it. One may think of it roughly as accelerating at right angles to Our course.”
“Yes, yes, I see that,” Captain King cut in, “but why do you assume that the resultant vectors must always be equal to our present vector?”
“Why, it need not be if the Captain decides otherwise,” Libby answered, looking puzzled, “but to apply a component that would reduce the resultant vector below our present speed would simply be to cause us to backtrack a little without increasing the scope of our present loci of possible destinations. The effect would only increase our flight time, to generations, even to centuries, if the resultant-”
“Certainly, certainly! I understand basic ballistics, Mister. But why do you reject the other alternative? Why not increase our speed? Why can’t I accelerate directly along my present course if I choose?”
Libby looked worried. “The Captain may, if he so orders. But it would be an attempt to exceed the speed of light. That has been assumed to be impossible-”
“That’s exactly what I was driving at: ‘Assumed.’ I’ve always wondered if that assumption was justified. Now seems like a good time to find out.”
Libby hesitated, his sense of duty struggling against the ecstatic temptations of scientific curiosity. “If this were a research ship, Captain, I would be anxious to try it. I can’t visualize what the conditions would be if we did pass the speed of light, but it seems to me that we would be cut off entirely from the electromagnetic spectrum insofar as other bodies are concerned. How could we see to astrogate?”
Libby had more than theory to worry him; they were “seeing” now only by electronic vision. To the human eye itself the hemisphere behind them along their track was a vasty black; the shortest radiations had dopplered to wavelengths too long for the eye. In the forward direction stars could still be seen but their visible “light” was made up of longest Hertzian waves crowded in by the ship’s incomprehensible speed. Dark “radio stars” shined at first magnitude; stars poor in radio wavelengths had faded to obscurity. The familiar constellations were changed beyond easy recognition. The fact that they were seeing by vision distorted by Doppler’s effect was confirmed by spectrum analysis; Fraunhofer’s lines had not merely shifted toward the violet end, they had passed beyond, out of sight, and previously unknown patterns replaced them.
“Hmm . . .” King replied. “I see what you mean. But I’d certainly like to try it, damn if I wouldn’t! But I admit it’s out of the question with passengers inboard. Very well, prepare for me roughed courses to type ‘0’ stars lying inside this trumpet-flower locus of yours and not too far away. Say ten light-years for your first search.”
“Yes, sir. I have. I can’t offer anything in that range in the ‘0’ types.”
“So? Lonely out here, isn’t it? Well?’
“We have Tau Ceti inside the locus at eleven light-years.” –
“A 05, eh? Not too good.”
“No, sir. But we have a true Sol type, a 02-catalog ZD9817. But it’s more than twice as far away.”
Captain King chewed a knuckle. “I suppose I’ll have to put it up to the elders. How much subjective time advantage are we enjoying?”
“I don’t know, sir.”
“Eh? Well~ work it out! Or give me the data and I will. I don’t claim to be the mathematician you are, but any cadet could solve that one. The equations are simple enough.” –
“So they are, sir. But I don’t have the data to substitute in the time-contraction equation . . -. because I have no way now to measure the ship’s speed. The violet shift is useless to use; we don’t know what the lines mean. I’m afraid we must wait until we have worked up a much longer baseline.”